Related papers: Scattering Theory and dispersive estimates for gen…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
We study the long-time behavior of solutions to nonlinear Schroedinger equations with some critical rough potential of inverse square type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property…
A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…
Slow, viscous flow in branched structures arises in many biological and engineering settings. Direct numerical simulation of flow in such complicated multi-scale geometry, however, is a computationally intensive task. We propose a…
In this article, we consider the infinite dimensional vector-valued resonant nonlinear Schr\"odinger system, which arises from the study of the asymptotic behavior of the defocusing nonlinear Schr\"{o}dinger equation on "wave guide"…
We derive the dispersion decay for solutions of the 1D discrete Schroedinger and wave equations. Based on previous works, we weaken the conditions on potentials.
Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schr\"{o}dinger equation for spatially varying effective mass, the simplest…
We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor…
We discuss the evaluation of the real part of the elementary amplitudes in the context of a multiple diffraction model for $pp$ elastic scattering earlier developed. The framework is based on the concepts of analyticity and polynomial…
We develop a mesoscale transport theory for the charge and spin degrees of freedom of itinerant carriers in a $d$-wave altermagnet. Our effective Lagrangian description is built upon the slave-boson formulation of the microscopic $t-J$…
The one-dimensional piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a dispersive fluid described by the nonlinear Schr\"odinger equation is analyzed.…
In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schr\"odinger equation with a potential of form \begin{align*} i\partial_t u+\Delta u- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy…
We obtain general bounds on scattering processes involving charged particles in 1+1 spacetime dimensions. After a general analysis we derive mostly numerical bounds on couplings in theories with $O(N)$ and $U(N)$ global symmetries. The…
We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\hbar=0$ this problem reduces to the well known problem of chaotic scattering.…
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy.…
Inflation correlators with massive exchanges are central observables of cosmological collider physics, and are also important theoretical data for us to better understand quantum field theories in dS. However, they are difficult to compute…
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
A general theory is developed to describe graphene with arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the minimal conductivity of…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…